Post by Harald HardersPost by Gregory L. HansenPost by Harald HardersPost by Michele DondiPost by mrlinuxHow can I get the tensor symbol, I mean the doublearrow over \epsilon ???
Are you sure that is "*the* tensor symbol"? I've never ever seen it in
print or in handwriting either...
And what exactly is a tensor? A scalar, a vector, ... Do you use the
same symbol for all stages/orders (what is the correct term in English)?
Usually the word tensor is used for something with at least two indices.
Scalars and vectors may be tensors, but they already have their own names.
So if someone mentions, e.g., a tensor force, you can be sure that he
doesn't mean a zeroeth-rank tensor force or a first-rank tensor force.
Ah, I know what a tensor is. But what I ment is that you should not use
the same symbol for all orders. I have learned a nomenclature for tensors
at university that uses simple underline for vectors, double underline
for second-rank tensors and a tilde under the symbol with the rank of
s = C .. e
= ~ =
4
(of course with a smaller 4 under the C). And of course, there is the
The tilde notation is new to me, but the underlines have always bugged
me. But I see nothing wrong with a single arrow for a vector, a double
arrow for a second-rank tensor, and a tilde over the symbol with the rank
of the tensor above it for higher-rank tensors. I'd probably be the only
person in the world using that particular convention, though.
Post by Harald Harderss_ij = C_ijkl e_kl
But for a single tensor, the index notations gives one component instead
of the whole tensor. And (s_ij) is the component matrix for a given
coordinate system, still not the whole tensor because you have to give
the coordinate system(s) to get the tensor itself.
If you're talking about one particular component, then you need to know
the basis for that to make any sense. But when you have all of them
together, it really doesn't matter. s_ij = C_ijkl e_kl no matter what
basis you use. s_11 or s_32 would depend on the basis, but that s_ij is
related to that particular sum doesn't.
Or another example, v_i = g_ij v^j, lowering an index written out as
components, or v = (g_ij) ...
Eh, I guess I don't know of notation that distinguishes a contravariant
from a covariant vector, except for where you put the index. Maybe that's
what underlines are good for.
--
"In any case, don't stress too much--cortisol inhibits muscular
hypertrophy. " -- Eric Dodd